Neutrino oscillations and big bang nucleosynthesis

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Abstract

We outline how relic neutrino asymmetries may be generated in the early universe via active-sterile neutrino oscillations. We discuss possible consequences for big bang nucleosynthesis, within the context of a particular 4-neutrino model.

Introduction

The implications of neutrino masses in cosmology and astrophysics are numerous. One fascinating effect, is that of relic neutrino asymmetries, which may be produced if there is mixing between active and sterile neutrino species [1].

Neutrino asymmetries are interesting since they affect big bang nucleosynthesis (BBN), altering the primordial helium yield. BBN is particularly sensitive to an asymmetry between the νe and ν̄e. Additionally, since the matter potential arising from forward scattering is proportional to the asymmetry, a large asymmetry will suppress active-sterile oscillation modes which could otherwise equilibrate sterile neutrino species around the time of BBN.

Section snippets

Relic neutrino asymmetries

First consider two-flavour mixing between an active neutrino, να, and a sterile neutrino, νs. For each neutrino flavour we define an asymmetryLα=nνα−nν̄αnγwhere nν and nγ are the neutrino and photon number densities, respectively.

The neutrino momentum distributions, N(p), are such thatn=∫N(p)dpand in thermal equilibrium are just given by Fermi-Dirac distributionsNeq(p)=12p21+exp(pT+μ̃).Here T is the temperature and μ̃≡μ/T, with μ being the neutrino chemical potential. In equilibrium, Lα is

Big bang nucleosynthesis and a four neutrino model

We wish to determine the impact of such asymmetry production on the BBN light element abundances, and in particular, on the helium yield. In general, the results are somewhat model dependent (compare, say, [7] with [8].)

The results are particularly sensitive to the size of the νe asymmetry, which directly affects the neutron/proton ratio through the reaction ratesλ(np)≃λ(nνepe)+λ(ne+pν̄e),λ(pn)≃λ(penνe)+λ(pν̄ene+).The n/p ratio determines the helium mass fraction YP via the equationdYPdt

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Invited talk at the NUFACT’01 workshop in Tsukuba, Japan, 24–30 May 2001.

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